Combat

The combat equation

The damage is always the same, independant from random variables. Of course if your guys stand above the enemies (e. g. when shooting from a cliff), they get an advantage.
There are a few consequences of the combat engine:

Get the axeman upgrade soon. Clubmen are almost as weak as villagers, and as soon as you have three of them, upgrade! You get more HP and more damage for that upgrade; clubmen do not have any chance against axemen.

When advancing to the tool age, upgrade armor first (for the axemen at the storage pit), not the weapons!
If you upgrade the armor, you'll have a 5/2 axeman; against a 5/0 axeman,
he needs 10 hits to kill him and will have 20 HP left. A 7/0 axeman on the other
hand needs 8 hits and will have only 10 HP left! This is a pretty large
difference. And this shows that you must upgrade the armor ASAP! You get a huge advantage by upgrading the armor early.
After the enemy has upgraded the armor too, it does not really matter
anymore what you upgrade.

Towers

Towers are much stronger than in Warcraft, but as soon as you get siege engines in the bronze age, they lose some of their power. A catapult tears down a tower really fast and has a far greater range. If you have a tower, make sure you have some troops (Cavalry or light infantry) to take out a catapult! A tower alone will not make a good defense.

The advantage that towers have is that you can get a lot of them without having to care about the unit limit. If you have reached the limit and want to build a wonder, use your excess resources for towers first! Build up a defense and then start constructing the wonder.

Your army

Catapults are really cool. They destroy towers and buildings fast, but are totally useless against moving targets. Make sure you have some infantry (hopelites) to protect the catapult! Hoplites are perfect for that job since they are very tough and almost as slow as the catapult. If you let someone get to the catapult, it is destroyed almost instantly. Heavy Catapults and Juggernaughts can destroy trees with "attack ground".

An army of hoplites can be taken out with archers, though. Because the archers are faster than the hopelites, they can always keep their distance. That's why you should have some cavalry to hunt the archers. Generally, a troop that contains all kinds of units (archers, infantry and cavalry) is the best. Like in other strategy games, it is obvious that you have to concentrate your forces on one spot to win. To make all guys attack the same opponent, click next to the enemy. The will walk towards him and charge him as soon as they see him. After he is killed, they will head to the next one. If you click at a guy, the units at the rear will stop as soon as that guy is dead.

Of course you always must make sure that you get enough resources for your army. Planning is crucial in AoE. If you get the "not enough houses" messages, you are in trouble. Make sure that does not happen, and try to have always some food for units.

Scouting is also important. You will not want to run into a bunch of towers. These scouts are really cheap and fast, so use them!

Research ballistics

This makes a huge difference. If an enemy comes into the range of a catapult, it will instantly fire. Without ballistics, the shot will land where the guy stood at the moment when the catapult fired. That's why you never hit a guy that is moving.

With ballistics, though, the catapult will estimate how far the guy will walk until the shot hits the ground and therefore get him (unless he changes the direction)! You will suddenly hit your enemies with catapults, only because you've researched ballistics. This is a huge power up, so go for it!

Monotheism

This lets you convert enemy buildings, but the priest has to get close to them. It is nice if your priests have an increased range, so you can try to convert enemy priests. This upgrade is not overwhelmingly powerful, but still worth the investment. It also lets you take over an enemy base instead of destroying it.

A cheap strategy on small maps

With the Shang and the Sumerian tribe, you can win with a "villager rush".
The Shang get 3 villagers instead of 2, and if you scout with your 3rd
villager and find your opponent soon, you can annihilate him by
outnumbering him by 50 %. The Sumerian villagers are as strong as Clubmen,
so you keep producing villagers without building a barracks and attack
before the opponent upgrades or even before he gets clubmen.

Both strategies are certainly not in the spirit of AoE and would produce
short games (5 minutes). I like short games (about half an hour
long) and duels where you can attack early, but "peon rushes" are cheap. I hope that the attributes of these two tribes will be tweaked in a way to prevent that (the bonuses for the Shang/Sumerian villagers are sky high now).